Computing invariant densities and metric entropy

We present a method fur accurately computing the metric entropy (or, equiva lently, the Lyapunov exponent) of the absolutely continuous invariant measu re mu for a piecewise analytic expanding Markov map T of the interval. We c onstruct atomic signed measures mu(M) supported on periodic orbits up to pe riod M, and prove that integral log \T'\ d mu (M) --> (h) over bar (mu) sup er-exponentially fast, We illustrate our method with several examples.